Transcription-activator-like effector (TALE)-based tools for base editing of nuclear and organellar DNA rely on double-stranded DNA deaminases, which edit substrate bases on both strands of DNA, reducing editing precision. Here, we present CyDENT base editing, a CRISPR-free, strand-selective, modular base editor. CyDENT comprises a pair of TALEs fused with a FokI nickase, a single-strand-specific cytidine deaminase and an exonuclease to generate a single-stranded DNA substrate for deamination. We demonstrate effective base editing in nuclear, mitochondrial and chloroplast genomes. At certain mitochondrial sites, we show editing efficiencies of 14% and strand specificity of 95%. Furthermore, by exchanging the CyDENT deaminase with one that prefers editing GC motifs, we demonstrate up to 20% mitochondrial base editing at sites that are otherwise inaccessible to editing by other methods. The modular nature of CyDENT enables a suite of bespoke base editors for various applications.